In
engineering and science it is often desirable to use the simplest possible
mathematical model that “does the job”. First-principles modeling or system
identification commonly result in unnecessarily high-dimensional mathematical
models. Model (order) reduction concerns systematic approximation of such
models. There are many advantages of working with models with a low-dimensional
state space. For example, low-dimensional models are easier to analyze and much
faster to simulate. Model reduction methods have successfully been used to
solve large-scale problems in areas such as control engineering, signal
processing, image compression, fluid mechanics, and power systems. In this
Ph.D. course, we give an introduction to some powerful available reduction
techniques, as well as to the required underlying mathematics.